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PubMed2005

Cramer-Rao bound and phase-diversity blind deconvolution performance versus diversity polynomials.

Information theoretic bounds on the estimated Zernike coefficients for various diversity phase functions are presented. We show that, in certain cases, defocus diversity may yield a higher Cramer-Rao lower bound (CRLB) than some other diversity phase functions. Using simulated images to evaluate the performance of the phase-diversity algorithm, we find that, for an extended scene and defocus diversity, the phase-diversity algorithm achieves the CRLB for known objects. Furthermore, the phase-diversity algorithm achieves the CRLB by a factor of approximately 2 for unknown objects.

Journal Article↗
PubMed2006

Application of self-deconvolution method to shift-and-add solar imaging.

A shift-and-add (SAA) operation is conducted to reconstruct a high-spatial-resolution image from atmospherically degraded solar images. The self-deconvolving data reconstruction algorithm is used to augment high-spatial-frequency components in solar speckle images and rectify the background component that results from the SAA operation. Self-deconvolved solar speckle images are shift and added and the resulting image shows high-spatial-resolution features.

Journal Article↗
PubMed1998

Superresolution and convergence properties of the expectation-maximization algorithm for maximum-likelihood deconvolution of incoherent images.

Computational optical-sectioning microscopy with a nonconfocal microscope is fundamentally limited because the optical transfer function, the Fourier transform of the point-spread function, is exactly zero over a conic region of the spatial-frequency domain. Because of this missing cone of optical information, images are potentially artifactual. To overcome this limitation, superresolution, in the sense of band extrapolation, is necessary. I present a frequency-domain analysis of the expectation-maximization algorithm for maximum-likelihood image estimation that shows how the algorithm achieves this band extrapolation. This analysis gives the theoretical absolute bandwidth of the restored image; however, this absolute value may not be realistic in many cases. Then a second analysis is presented that assumes a Gaussian point-spread function and a specimen function and shows more realistic behavior of the algorithm and demonstrates some of its properties. Experimental results on the superresolving capability of the algorithm are also presented.

Algorithms↗
PubMed2006

High-order statistical blind deconvolution of spectroscopic data with a Gauss-Newton algorithm.

The spectroscopic data recorded by a dispersion spectrophotometer are usually degraded by the response function of the instrument. To improve the resolving power, double or triple cascade spectrophotometers and narrow slits have been employed, but the total flux of the radiation available decreases accordingly, resulting in a lower signal-to-noise ratio (SNR) and a longer measurement time. However, the spectral resolution can be improved by mathematically removing the effect of the instrument response function. A high-order statistical Gauss-Newton algorithm is proposed to blindly deconvolve the measured spectroscopic data. The true spectrum and the instrument response function are estimated simultaneously. Experiments on artificial and real measured spectroscopic data demonstrate the feasibility of this method.

Journal Article↗
PubMed2025

ChromaFactor: Deconvolution of single-molecule chromatin organization with non-negative matrix factorization.

The investigation of chromatin organization in single cells holds great promise for identifying causal relationships between genome structure and function. However, analysis of single-molecule data is hampered by extreme yet inherent heterogeneity, making it challenging to determine the contributions of individual chromatin fibers to bulk trends. To address this challenge, we propose ChromaFactor, a novel computational approach based on non-negative matrix factorization that deconvolves single-molecule chromatin organization datasets into their most salient primary components. ChromaFactor provides the ability to identify trends accounting for the maximum variance in the dataset while simultaneously describing the contribution of individual molecules to each component. Applying our approach to two single-molecule imaging datasets across different genomic scales, we find that these primary components demonstrate significant correlation with key functional phenotypes, including active transcription, enhancer-promoter distance, and genomic compartment. Also, we find that some bulk trends exist at the single-cell level, but only in a small fraction of cells, suggesting that critical changes in genome organization may be driven by specific rare subpopulations rather than occurring uniformly across all cells. ChromaFactor offers a robust tool for understanding the complex interplay between chromatin structure and function on individual DNA molecules, pinpointing which subpopulations drive functional changes and fostering new insights into cellular heterogeneity and its implications for bulk genomic phenomena.

Animals↗
PubMed2002

Excitation pulse deconvolution in luminescence lifetime analysis for oxygen measurements in vivo.

Oxygen-dependent quenching of phosphorescence has been proven to be a valuable tool for the measurement of oxygen concentrations both in vitro and in vivo. For biological measurements the relatively long lifetimes of phosphorescence have promoted time-domain-based devices using xenon arc flashlamps as the most common excitation light source. The resulting complex form of the excitation pulse leads to complications in the analysis of phosphorescence lifetimes and ultimately to errors in the recovered pO2 values. Although the problem has been recognized, the consequences on in vivo phosphorescence lifetime measurements have been neglected so far. In this study, the consequences of finite excitation flash duration are analyzed using computer simulations, and a method for the recovery of phosphorescence decay times from complex photometric signals is presented. The analysis provides an explanation as to why different calibration constants are reported in the literature and presents a unified explanation whereby calibration constants are not solely a property of the dye but also of the measuring device. It is concluded that complex excitation pulse patterns without appropriate analysis methods lead to device-specific calibration constants and nonlinearity and can be a potent source of errors when applied in vivo. The method of analysis presented in this article allows reliable phosphorescence lifetime measurements to be made for oxygen pressure measurements and can easily be applied to existing phosphorimeters.

Algorithms↗
PubMed1998

Deconvolution of chemiluminescent emission curve associated with phagocytosis into three logarithmic normal distributions.

The chemiluminescent emission reaction dependence on the activity of phagocytosis is well known. However, this method is not used to diagnostically in clinical assessment because the relationship between phagocytizing activity and chemiluminescent intensity has not been clearly established. Therefore, we attempted to analyze quantitatively the chemiluminescent emission curve by the phagocytosis of leukocytes. Mathematical assessment of the emission curve with respect to time was performed by fitting the curve to several regression models using the unweighed non-linear least squares method. A triple logarithmic normal distribution model provided a reasonable goodness of fit to the measured emission curve. The first component, about 5% of the calculated total counts, was assumed to arise from monocytes activity, the second component, about 20% from eosinocytes activity and the third component, up to 75%, from neutrophils activity. This method seems promising as a means for assaying whole blood without the need for pretreatment and for the providing a valid index that is independent of the technical differences between laboratories.

Data Interpretation, Statistical↗
PubMed2026

Deconvolution of evolutionary architecture unmasks a high-risk, subclonal-rich subtype in treatment-naive small cell lung cancer.

BACKGROUND: Intratumoral heterogeneity (ITH) drives therapeutic resistance in small cell lung cancer (SCLC). However, conventional single-sample analysis has limited horizontal, cross-patient comparisons, leaving the overarching evolutionary architecture in treatment-naive tumors poorly understood. This study aims to deconvolve these architectures to identify clinically relevant evolutionary subtypes. METHODS: We analyzed whole-exome sequencing data from 41 treatment-naive SCLC patients. To overcome the cross-patient comparability bottleneck, we developed a novel probabilistic framework using a refined Gaussian Mixture Model (GMM). This standardized subclonal structures into four hierarchical strata, enabling the identification of evolutionary subtypes via unsupervised clustering. To address the scarcity of SCLC public data, prognostic concordance was robustly explored in The Cancer Genome Atlas (TCGA) lung squamous cell carcinoma (LUSC) based on shared smoking etiology, with lung adenocarcinoma (LUAD) serving as a negative control. RESULTS: The cohort robustly segregated into "Clonal-dominant" (Group 1, n=28) and "Subclonal-rich" (Group 2, n=13) subtypes. Group 1 evolution was primarily driven by tobacco signatures (SBS4). Conversely, Group 2 exhibited late-stage acquisition of a DNA mismatch repair deficiency (MMRd) signature (SBS15), fueling trace subclonal diversification. Clinically, Group 2 demonstrated a significantly lower objective response rate (ORR) to platinum-based regimens (25.0% vs. 81.3%, P=0.02). Furthermore, the Subclonal-rich architecture independently predicted inferior overall survival (OS) [adjusted hazard ratio (adj. HR) =2.93, P=0.02], driven predominantly by limited-stage disease. Cross-cancer analysis validated this histology-dependent, high-heterogeneity adverse pattern in early-stage LUSC but not in LUAD. CONCLUSIONS: This hypothesis-generating study demonstrates that a "Subclonal-rich" architecture, driven by acquired MMRd, identifies high-risk, chemo-resistant SCLC. Our GMM approach suggests that pre-existing heterogeneity may serve as a potential, histology-dependent prognostic marker that warrants prospective validation for tailoring future therapeutic regimens.

Gaussian Mixture Model (GMM)↗